Matt needs to put a fence around a garden in his backyard. The perimeter is 104 meters. The length is 6 meters more than the width.
Matt wrote the first let statement. Fill in the blank below to complete the second let statement.
Let w = the width
Let = the length
Write an equation below that Matt can use to find the length and the width and solve it. What are the dimensions of the garden?

Question

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jitumahi76 jitumahi76 · Answer 1 · 2020-01-16T15:44:11+01:00

Answer:

The equation is [tex]Perimeter=2(2w+6)[/tex].

The length is 29 m and width is 23 m of the garden.

Step-by-step explanation:

Given,

Perimeter = 104 m

Solution,

Let 'w' = the width

Let 'l' = the length

Since the garden is in the form of rectangle.

Now we know that the perimeter of rectangle is 2 times the sum of length and width.

We can frame it as;

[tex]Perimeter=2(l+w)[/tex]

According to question, the length is 6 meters more than the width.

So we can say that;

[tex]l=w+6[/tex]

Now we substitute the value of 'l' and get;

[tex]Perimeter=2(l+w)=2(w+6+w)=2(2w+6)[/tex]

Hence The equation is [tex]Perimeter=2(2w+6)[/tex].

Now we solve the equation by putting the values and get;

[tex]2(2w+6)=104\\\\2w+6=\frac{104}{2}=52\\\\2w=52-6=46\\\\w=\frac{46}{2}=23\ m[/tex]

[tex]l=w+6=23+6=29\ m[/tex]

Hence The length is 29 m and width is 23 m of the garden.